Let ϕ(t) be the characteristic function, defined as the Fourier transform of the probability density function P(x) using Fourier transform parameters a = b = 1, ϕ(t) | = | ℱ_x[P(x)](t) | = | integral_(-∞)^∞ e^(i t x) P(x) d x. The cumulants κ_n are then defined by ln ϕ(t) congruent sum_(n = 1)^∞ κ_n (i t)^n/(n!) (Abramowitz and Stegun 1972, p. 928).

characteristic function | cumulant-generating function | Fourier transform | k-statistic | kurtosis | mean | moment | Sheppard's correction | skewness | unbiased estimator | variance